- Author
- Bram Vancraeynest-De Cuiper (UGent) , Jacob C Bridgeman (UGent) , Nicolas Dewolf (UGent) , Jutho Haegeman (UGent) and Frank Verstraete (UGent)
- Organization
- Project
-
- ERQUAF (Entanglement and Renormalisation for Quantum Fields)
- QUTE (Quantum tensor networks and entanglement)
- A high-performance tensor network library for classical and quantum many body physics
- An entanglement perspective on generalized symmetries, dualities and anomalies
- Abstract
- We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional lattice are considered together with an additional 'vertical reflection', which we take to be an on-site $\mathbb{Z}_2$ symmetry. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions. We furthermore construct explicit renormalization group fixed-point wave functions for symmetry-protected topological phases with global on-site symmetries, possibly combined with time-reversal and parity symmetry. En route, we demonstrate how group cohomology can be computed using the Smith normal form.
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8763020
- MLA
- Vancraeynest-De Cuiper, Bram, et al. “One-Dimensional Symmetric Phases Protected by Frieze Symmetries.” ArXiv:2202.12880, 2022.
- APA
- Vancraeynest-De Cuiper, B., Bridgeman, J. C., Dewolf, N., Haegeman, J., & Verstraete, F. (2022). One-dimensional symmetric phases protected by frieze symmetries.
- Chicago author-date
- Vancraeynest-De Cuiper, Bram, Jacob C Bridgeman, Nicolas Dewolf, Jutho Haegeman, and Frank Verstraete. 2022. “One-Dimensional Symmetric Phases Protected by Frieze Symmetries.” ArXiv:2202.12880.
- Chicago author-date (all authors)
- Vancraeynest-De Cuiper, Bram, Jacob C Bridgeman, Nicolas Dewolf, Jutho Haegeman, and Frank Verstraete. 2022. “One-Dimensional Symmetric Phases Protected by Frieze Symmetries.” ArXiv:2202.12880.
- Vancouver
- 1.Vancraeynest-De Cuiper B, Bridgeman JC, Dewolf N, Haegeman J, Verstraete F. One-dimensional symmetric phases protected by frieze symmetries. arXiv:2202.12880. 2022.
- IEEE
- [1]B. Vancraeynest-De Cuiper, J. C. Bridgeman, N. Dewolf, J. Haegeman, and F. Verstraete, “One-dimensional symmetric phases protected by frieze symmetries,” arXiv:2202.12880. 2022.
@misc{8763020,
abstract = {{We make a systematic study of symmetry-protected topological gapped phases of
quantum spin chains in the presence of the frieze space groups in one dimension
using matrix product states. Here, the spatial symmetries of the
one-dimensional lattice are considered together with an additional 'vertical
reflection', which we take to be an on-site $\mathbb{Z}_2$ symmetry. We
identify seventeen distinct non-trivial phases, define canonical forms, and
compare the topological indices obtained from the MPS analysis with the group
cohomological predictions. We furthermore construct explicit renormalization
group fixed-point wave functions for symmetry-protected topological phases with
global on-site symmetries, possibly combined with time-reversal and parity
symmetry. En route, we demonstrate how group cohomology can be computed using
the Smith normal form.}},
author = {{Vancraeynest-De Cuiper, Bram and Bridgeman, Jacob C and Dewolf, Nicolas and Haegeman, Jutho and Verstraete, Frank}},
language = {{eng}},
series = {{arXiv:2202.12880}},
title = {{One-dimensional symmetric phases protected by frieze symmetries}},
year = {{2022}},
}